/ Semantics on
And the gm variation is caused by bias voltage modulation.
So the bias voltage modulation is the root of all evil and gm variation, or more precisely, effective gm variation, is just a consequence.
Gm varies in a way as depicted, simply because I have included the bias voltage in the definition of gm.
If we define gm as the sum of gm of the top respectively bottom tranny itself, thus the bias voltage not counted, we get a completely different picture. But that's not a realistic approach, because in a real amp, we can't ignore or exclude the effect of the bias voltage.

I disagree with the "bias modulation" approach. The most logical way to discuss this distortion type is to consider the OPS gain vs. Vin dependency (or "gain modulation" if you prefer). Plot the OPS gain (always < 1) vs. the OPS input voltage Vin and you'll get the whole picture. Then think Gain=Rload*gm, valid at both small and large signal, therefore you have an equivalent "transconductance modulation" effect. An equivalent "bias voltage modulation" doesn't help as much understanding the causality beyond this distortion type.

The "gm doubling" denomination is confusing, it should be "gm variation".

There is a significat difference between bipolars and mosfet OPSs. If the mosfets are (auto)biased far away from the subthreshold conduction region (where Id(Vgs) is as much exponential as Ic(Vbe)), then the "gm variation" distortions (excluding the gm drop at high currents) are much smaller. When discussing dependencies on the OPS Iq, are you sure you are considering bipolars, rather than mosfets?

As a side note, "switching distortions" are only important at HF, where storage effects in bipolars can no longer be ignored. See the Leach paper I quoted above.

Let us try to summarize the problem in terms acceptable to everyone (I think all the participants to this discussion agree in fact on the core nature of the problem, but not on its semantic description).

When only (ideal) semiconductor junctions are present, no serious problem exists: the resulting transconductance is the sum of all the transconductances of active elements present, whatever their polarity, and when the current is transferred from one side to the other, the transconductance remains identical.
That is not true anymore when class B currents become large, but practically this effect is relatively minor, given the typical bias current and output load magnitude of "normal" amplifiers.

A more serious problem occurs with "normal" values of emitter resistors: if we simplify the problem and decide they dominate the output resistance, the output resistance in class A becomes ~Re/2, and in class B ~Re.
That's where the (so called) gm doubling effect comes from.

Ideally, both effects should be taken into account, but there is anyway a mitigating effect: the OPS is normally not voltage-driven (there are exceptions).
Such differences should therefore be mostly accessory, except for the frequency compensation which renders the drive voltage-mode at higher frequencies.
Are the differences that important?

/ Semantics on
And the gm variation is caused by bias voltage modulation.

Indeed but this "bias voltage modulation" is nothing else than the
output current dependant voltage drop through RE and Re wich
will add/substraxt to the requested Vbe once the output current
start varying , then we can interpret it as the varying gm being the
cause of Vbe modulation.

Quote:

Originally Posted by Waly

The most logical way to discuss this distortion type is to consider the OPS gain vs. Vin dependency (or "gain modulation" if you prefer). Plot the OPS gain (always < 1) vs. the OPS input voltage Vin and you'll get the whole picture. Then think Gain=Rload*gm, valid at both small and large signal, therefore you have an equivalent "transconductance modulation" effect. An equivalent "bias voltage modulation" doesn't help as much understanding the causality beyond this distortion type.

Agree with this , set apart the Gain formula but the reasonning
seems right to me.

When looking at the output stage , Gain = output/input = RL/(RL + 1/gm) ,
we can immediatly see that if gm is constant there will be
no distorsion but if gm is varying with output current then
the gain will vary as well , hence there will be distorsion.

When looking at the output stage , Gain = output/input = RL/(RL + 1/gm) ,we can immediatly see that if gm is constant there will be no distorsion but if gm is varying with output current then the gain will vary as well , hence there will be distorsion.

What you did is replaging the device gm (for Re=0, which I was discussing) with an equivalent gm for the device + Re. This is a classic transformation that, as you said, doesn't change the effect.

Indeed but this "bias voltage modulation" is nothing else than the output current dependant voltage drop through RE and Re wich will add/substraxt to the requested Vbe once the output current
start varying , then we can interpret it as the varying gm being the
cause of Vbe modulation.
[...]
When looking at the output stage , Gain = output/input = RL/(RL + 1/gm) ,
we can immediatly see that if gm is constant there will be
no distorsion but if gm is varying with output current then
the gain will vary as well , hence there will be distorsion.
[...]
There is no Re that is taken into account , actualy that is the
formulae for Re = 0.

Now, let's plot this stuff and look at the black curve, which depicts the combined gm (of top and bottom tranny). Contrary to my previous post of gm, the green curve, this one doesn't show the 'doubling' at large currents. Instead, only a small increase in the crossover zone. This is because the circuit is a bit over biased (which is another story).
Despite the fact we have taken into account the effect of Vbe, RE' and RE, this kind gm does not explain the excess of distortion caused by a sliding bias.
Please tell me what I did wrong.

The usual confusion between a small signal, linearized, and a large signal analysis. gm=Ic/26mV holds for small signal only. For large signal, Gm(0)=gm/2 where "0" stands for Vo=0. In fact, Gm depends strongly on the output level Vo (otherwise, for example, a bipolar oscillator would not work).

There is no simple way to calculate the large signal transconductance. The large signal analysis of an emitter follower with Re does not have any known analytical closed solution.

I wrote: gm ~=Ic/26mV and notice the tilde.
Whether this equation is correct doesn't matter, as I didn't use it for any calculation at all. My simulator did the calculations, which also takes care of large signal and other effects. And please don't start whining again about the accuracy of simulators. For the purpose at hand they are accurate enough.

The point is that the composite gm of the bipolar output trannies plus emitter resistors did not reveal the gm doubling at large currents. That means you can't use it for explaining the distortion. Perhaps you forgot it, but we are talking about the real cause of distortion: is it bias voltage modulation or is it gm modulation. According to my last plot (black curve) it is not gm modulation.

edit: the astute reader would notice that the 'green' gm curve does show gm doubling. So, wtf are we talking about?
Well, the 'green' gm has taken into account the effect of bias voltage modulation, while the 'black' gm does not.